The Greenland Ice Sheet Response to Transient Climate Change

DIANDONG REN* AND RONG FU

Jackson School of Geosciences, The University of Texas at Austin, Austin, Texas

LANCE M. LESLIE

School of Meteorology, University of Oklahoma, Norman, Oklahoma, and Australian Sustainable Development Institute,

Curtin University, Perth, Western Australia, Australia

JIANLI CHEN

Center for Space Research, The University of Texas at Austin, Austin, Texas

CLARK R. WILSON

Jackson School of Geosciences, and Center for Space Research, The University of Texas at Austin, Austin, Texas

DAVID J. KAROLY

School of Earth Sciences, University of Melbourne, Melbourne, Victoria, Australia

(Manuscript received 5 May 2010, in final form 14 October 2010)

ABSTRACT

This study applies a multiphase, multiple-rheology, scalable, and extensible geofluid model to the Greenland Ice Sheet

(GrIS). The model is driven by monthly atmospheric forcing from global climate model simulations. Novel features of the

model, referred to as the scalable and extensible geofluid modeling system (SEGMENT-Ice), include using the full Navier–

Stokes equations to account for nonlocal dynamic balance and its influence on ice flow, and a granular sliding layer between

the bottom ice layer and the lithosphere layer to provide a mechanism for possible large-scale surges in a warmer future

climate (granular basal layer is for certain specific regions, though). Monthly climate of SEGMENT-Ice allows an investigation

of detailed features such as seasonal melt area extent (SME) over Greenland. The model reproduced reasonably well the

annual maximum SME and total ice mass lost rate when compared observations from the Special Sensing Microwave Imager

(SSM/I) and Gravity Recovery and Climate Experiment (GRACE) over the past few decades.

The SEGMENT-Ice simulations are driven by projections from two relatively high-resolution climate models, the NCAR

Community Climate System Model, version 3 (CCSM3) and the Model for Interdisciplinary Research on Climate 3.2, high-

resolution version [MIROC3.2(hires)], under a realistic twenty-first-century greenhouse gas emission scenario. They suggest

that the surface flow would be enhanced over the entire GrIS owing to a reduction of ice viscosity as the temperature increases,

despite the small change in the ice surface topography over the interior of Greenland. With increased surface flow speed, strain

heating induces more rapid heating in the ice at levels deeper than due to diffusion alone. Basal sliding, especially for granular

sediments, provides an efficient mechanism for fast-glacier acceleration and enhanced mass loss. This mechanism, absent from

other models, provides a rapid dynamic response to climate change. Net mass loss estimates from the new model should reach

;220 km3 yr21 by 2100, significantly higher than estimates by the Intergovernmental Panel on Climate Change (IPCC)

Assessment Report 4 (AR4) of ;50–100 km3 yr21. By 2100, the perennial frozen surface area decreases up to ;60%, to ;7 3

105 km2, indicating a massive expansion of the ablation zone. Ice mass change patterns, particularly along the periphery, are

very similar between the two climate models.

* Current affiliation: Australian Sustainable Development Institute, Curtin University, Perth, Western Australia, Australia.

Corresponding author address: Dr. Diandong Ren, Australian Sustainable Development Institute, Curtin University, Perth WA 6845,

Australia.

E-mail: diandongren1972@mail.utexas.edu.

1 JULY 2011 R E N E T A L . 3469

DOI: 10.1175/2011JCLI3708.1

� 2011 American Meteorological Society

1. Introduction

The Greenland Ice Sheet (GrIS), because of its large

size, unique location, and strong thermal contrast with

adjacent open waters, has a strong influence on large-

scale atmospheric variations (Wallace 2000; Bromwich

et al. 1999), and its melting has a potential influence on

global sea level rise (Yin et al. 2009). Its response to a

warming climate and the resultant influence on global

and regional climate is widely acknowledged (Thomas

2001; Steffen and Box 2001). Compared with Antarctica,

the GrIS has a faster mass turnover. Marine-terminating

glacier calving, together with surface and basal melting

from fast-glaciers at the periphery of the GrIS, drain large

volumes of ice. Recent findings indicate that glacier–

ocean interaction also played an important role in the

recent acceleration of the outlet glaciers of Greenland

(Straneo et al. 2010; Rignot et al. 2010). Discharge rates

are determined largely by fast-glacier dynamics, which

presently are poorly understood (Abdalati and Steffen

2001) and inadequately represented in previous ice dy-

namics models.

Remote sensing measurements (Krabill et al. 2000;

Abdalati and Steffen 2001; Rignot and Kanagaratnam

2006) have revealed increased flow speeds, widespread

melting of the ice surface, and accelerating mass loss from

peripheral outlet glaciers. These observations suggest that

ice mass loss has accelerated in the last decade, with ice

flow speeds significantly higher than previously estimated.

Ice core data during glacial periods from Summit of

the GrIS indicate that temperature and accumulation rates

can increase significantly over periods ranging from years

to decades (Alley 1993), suggesting that observed melting

could be influenced by large natural variability on inter-

annual to decadal scales, in addition to rapid surface tem-

perature warming caused by anthropogenic forcing.

The response of the GrIS to climate change has been

investigated in sensitivity studies (e.g., Kuhn 1981; Ambach

1985) using idealized future atmospheric conditions, pa-

leoclimate scenarios (Huybrechts et al. 1991; Van de Wal

and Oerlemans 1997; Greve 2000), or temperature and

precipitation rates derived from climate models (Ohmura

et al. 1996). For example, the Intergovernmental Panel

on Climate Change (IPCC) Assessment Report 4 (AR4),

using a simple surface mass balance estimation for sea level

predictions, states that ‘‘quantitative projections of how

much the accelerated ice flow would add (to sea level rise)

cannot be made with confidence, owing to limited under-

standing of the relevant processes (FAQ Section 5.1).’’

Here we introduce an ice sheet dynamics model, the

scalable and extensible geofluid modeling system

(SEGMENT-Ice), which is driven by monthly surface

meteorological conditions provided by two relatively

high-resolution coupled general circulation models

(CGCMs) that participated in the IPCC AR4 (Hegerl

et al. 2007). A key new feature of the ice dynamics

model is a granular sliding layer between the bottom ice

layer and the lithosphere layer. The treatment is based on

recent developments in granular material rheology (Jop

et al. 2006). Because a lubricating layer of basal sedi-

ments present between the ice and the bedrock enhances

ice flow. A lubricating layer of basal sediments that is

present between the ice and the bedrock enhances the ice

flow and is a mechanism for large scale surges (MacAyeal

1992; Alley et al. 2006) in a warming future world.

SEGMENT-Ice was validated against satellite observa-

tions of total ice mass loss, surface melting area and el-

evation changes over Greenland in the recent decade.

The model then is used to determine future mass loss

and ice flow by the middle and end of the twenty-first

century using CGCM simulations under the A1B scenario

from the IPCC Special Report on Emissions Scenarios

(Nakicenovic and Swart 2000).

2. Data and methods

a. Digital elevation map, geothermal heat flux, andinitial ice temperature field

We use the surface topography [digital elevation map

(DEM)] and bedrock topography provided by Bamber

et al. (2001). The surface DEM is used to calculate strain,

stress, and surface slope. The latter in turn is used to es-

timate the meltwater redistribution. We use the original

5-km resolution of ice thickness and DEMs. The total ice

volume is 2.89 3 106 km3, close to the estimate of 2.81 3

106 km3 from Weng (1995), but significantly larger than

a previously quoted value (Ohmura et al. 1996; Weidick

1995) of 2.6 3 106 km3.

In situ measurements of ice profile temperatures are very

limited over Greenland. Therefore, we use the initial tem-

perature field from a paleoclimate simulation of the

Simulation Code for Polythermal Ice Sheets (SICOPOLIS;

Greve 2000), which covers the entire last glacial–interglacial

cycle (150-kyr BP; Greve 2005), to initialize the model.

The ice sheet temperature regime is controlled by both

the surface energy balance history and the spatial distri-

bution of geothermal heat flux (Greve 2005; Cuffey et al.

1995; Pollack et al. 1993). For future simulations, we hold

the geothermal pattern constant as in the hf_pmod2 ex-

periment of Greve (2005) because it provides a realistic

representation of current Greenland ice sheet geometry

and flow fields.

b. GRACE and IceSAT datasets

The Gravity Recovery and Climate Experiment

(GRACE) satellite mission data are used to estimate ice

3470 J O U R N A L O F C L I M A T E VOLUME 24

mass changes over Greenland (Chen et al. 2006). Monthly

gravity data are used from the Center for Space Research

GRACE release 4 (CSR-RL04) to compute the total ice

mass change for the period April 2002–September 2008.

The GRACE cannot provide spatial resolution finer

than several hundred kilometers (Velicogna and Wahr

2006), preventing the evaluation of detailed spatial features

simulated by the ice model using the GRACE data. The

Geoscience Laser Altimeter System (GLAS) instrument

on the Ice, Cloud, and land Elevation Satellite (ICESat)

level-II GrIS altimetry data (Zwally et al. 2003) provide

along-track seasonal ice sheet surface elevations. A subset

of these data is used from samples that are not contami-

nated by thick clouds, wet snow surface, and instrument

problems. First, we average the pixels of years 2003 and

2007 into 5-km boxes and then compare the maps from

these two years to determine ice sheet elevation changes.

c. Climate model output

The horizontal model resolution improves the re-

gional simulation of precipitation (Genthon 1994) and,

for Greenland, may lead to overestimation of precipi-

tation (Ohmura et al. 1996). Thus, two coupled general

circulation models (CGCMs) with relatively fine hori-

zontal resolutions, that is, the National Center for Atmo-

spheric Research (NCAR) Community Climate System

Model, version 3 (CCSM3) (Collins et al. 2007, ;1.48) and

Model for Interdisciplinary Research on Climate 3.2

(MIROC3.2) (Hasumi and Emori 2004, ;1.1258), were

chosen. These CGCMs provide all the input variables

needed by SEGMENT-Ice (Ren et al. 2007), that is,

monthly-mean near surface air temperature, precipitation

rate, surface (skin) temperature, surface pressure, 2-m

wind speed, and all six components of radiation for de-

termining the surface energy balance. Our estimates of the

warming effects on ice sheet melting are based on the

Special Report on Emissions Scenarios (SRES) A1B

scenario, which assumes a balanced energy source in

a future world of rapid economic growth. This scenario

is chosen primarily because it reflects the most recent

trends in the driving forces of emissions.

Snow accumulation timing is a critical parameter for

determining ice sheet mass balance (Steffen and Box

2001). We use monthly temperature increment to deter-

mine snow accumulation anomalies and additional

melting relative to the control period (the 1961–90 datum

period, Ren et al. 2007) as inputs to the ice flow model, to

minimize potential biases in these variables produced by

climate models.

d. NCEP–NCAR reanalysis monthly means

Coupled ocean–atmospheric climate models do not

resolve realistic phases for interannual and decadal

climate variations. Thus, they cannot be used as climate

forcing for our ice model validation against observations

on interannual to decadal scales. More realistic climate

forcing is provided by the National Centers for Environ-

mental Prediction (NCEP)–NCAR reanalysis (Kalnay

et al. 1996). The reanalyses are widely used by climate

research community as a surrogate for real observations

on large spatial scale. Reanalysis data is available only

from 1948, too short a period to spin up the ice model, so

we use twentieth-century simulations of the CGCMs to

initialize the model, then blend in relevant atmospheric

parameters from the reanalyses (http://www.cdc.noaa.gov/

data/gridded/data.ncep.reanalysis.derived.surfaceflux.html),

starting from 1948.

e. Ice dynamics model

The new ice model, SEGMENT-Ice, is a continuum

mechanical formulation starting from a force balance

model (Van der Veen 1999) and is improved by including

acceleration, viscous friction, and advection terms (Ren

et al. 2008). SEGMENT-Ice retains the full Navier–

Stokes equations to account for nonlocal dynamic bal-

ance effects in ice flow. This differs from most previous ice

dynamics models, which assume that the ice sheet is locally

in dynamic equilibrium (e.g., van de Wal and Oerlemans

1994; Huybrechts 1994; Van der Veen and Whillans 1989).

The thermomechanically coupled scheme is designed and

implemented as one integral component of a scalable and

extensible geofluid modeling system (SEGMENT; Ren

et al. 2011, 2010). This model provides prognostic fields of

the driving and resistive forces and describes the flow

fields and the dynamic evolution of thickness profiles of

the medium. The inner ice domain follows Glen’s (1955)

ice rheology. A granular layer is allowed between ice and

unfractured bed rock. Granular viscosity parameteriza-

tion is based on Jop et al. (2006). Many other ice models use

only ice over bed rock configuration, whereas SEGMENT-

Ice allows ice–granular material–bedrock configuration

for regions with granular material presence—mostly re-

gions with significant basal melt. Formulation of the gran-

ular law; justification of the granular layer, the omission

of isostatic rebound; discussion of consistent choices of

ice constitutive law and Weertman basal sliding; and new

approaches in parameterizing of surface melting, runoff,

and the crevasse enhancement of basal sliding are de-

scribed in the appendix.

The horizontal grid spacing of the ice dynamics model

is 5 km. The atmospheric parameters are downscaled to

spatially match the ice geometry data, to integrate the

ice dynamics model at 5-km grid spacing. There are 81

vertically stretched layers to delineate the ice thickness,

including one lithosphere layer at the bottom and an

adjacent granular layer. For areas with granular material

1 JULY 2011 R E N E T A L . 3471

thickness less than 5 cm, the granular layer is nominal and

granular rheology is not activated. The integration time

step is one day, with atmospheric forcing updated every

month. This temporal configuration allows an examina-

tion of surface melting extent because, for most of the

surface area, melting is seasonal. The annual time step, as

in most paleoclimate studies, cannot resolve this dynamic

feature of melt surface area, which responds sensitively to

climate warming. For ice grounded on land or extending

to the sea, we apply zero-stress lateral boundary condi-

tions. The bedrock viscosity is 8 3 1020 Pa s.

It is critical to obtain a steady flow, in agreement with

the ice geometry and temperature regime, before ap-

plying the transient climate forcing to project the future

state of the ice sheet. The following spinup strategy is

used, starting from a zero velocity field at the given ice

geometry and temperature field. Because we are dealing

with full Navier–Stokes code in combination with a shear-

thinning rheological law, it is important to set a suitable

asymptotic viscosity for grid points with effective strain

rate less than 1028 s21. At present, all rheological re-

lationships in the modeling community are based on

experimental shear–strain diagrams. However, because

laboratory ice mechanics experiments must be completed

in a reasonable time span, it currently lacks a shear–strain

diagram extending to the very small strain rate regime

(,1028 s21 also is termed an impractical slow strain rate,

see, e.g., Goldsby 2006). The viscosity for those ‘‘still’’

grids is set to (1 2 T/Tp)1/5 3 1014 Pa s, with Tp being the

pressure melt temperature. As the integration continues,

the effective strain rate will be greater than 1028 s21 and

regular parameterization of the viscosity then will be

activated. Depending on the detailed numerics, the exact

number of integrations may vary significantly. However,

the evolution is that the bottom layer reaches stability first,

and then gradually the shallower layer reaches a steady

state. Upon reaching a steady flow field, the dynamics and

thermodynamics and the evolution of the free surface are

solved in a fully thermomechanically coupled manner.

3. Model validation

The seasonal surface melting extent (SME) on the GrIS

has been observed by satellites since 1979 and shows an

increasing trend (see Figs. 1a and 1b, chapter 6 in Symon

et al. 2005). SME is directly influenced by changing cli-

mate conditions at the ice surface and is a useful rep-

resentation of the ablation zone temporal variability.

The monthly integration time step in SEGMENT-Ice

ice model allows estimation and validation of the sum-

mer maximum SME. Contrary to the widespread belief

that melting only is related to air temperature, field ex-

periments (L. Thompson 2007, personal communication)

demonstrate clearly that melting occurs even with air

temperatures well below the freezing point. Normal ranges

of the stability-dependent eddy transfer coefficient and

the near-surface mean wind speed prevent a near-surface

temperature of 258C while net energy input for a mol-

ten ice surface remains positive (chapter 7 in Hambrey

and Alean 2004). Thus, the ‘‘near-surface forcing crite-

ria’’ for surface melting is stipulated in our model as a 2-m

air temperature greater than 258C and net radiation

larger than 170 W m22. This formulation was evaluated

by comparing the modeled seasonal maximum SME

forced by NCEP–NCAR reanalysis with those observed

by the Special Sensing Microwave Imager (SSM/I) for

1992 and 2002, respectively. In both years, the general

patterns of modeled maximum SME agree well with

observations (Fig. 1). In 1992, melting was confined to

the narrow peripheral areas well below 2000-m eleva-

tion, except for southern and mideastern Greenland,

where the melting extended close to the 2000-m elevation

contour. The model reproduces this pattern with some

overestimation of melting in southwest and northeast

Greenland. In 2002, the maximum SME crept up to

2000-m elevation in northern Greenland and approached

the 2500-m elevation in southern and mideastern Green-

land. Consequently, the area of maximum SME increased

from ;0.34 million in 1992 to ;0.58 million km2 in 2002.

The simulated maximum SME shows a similar pattern,

although with an underestimation of the melting be-

tween the Summit and South Dome and the northeast

corner of Greenland. Overall, the model realistically

captures the spatial pattern and change of maximum

SME for the period of 1992–2002, with a slight under-

estimation of the SME rate of increase.

Figure 2 compares the modeled ice surface elevations

with those derived from the GLAS/ICEsat, for the period

of 2002–07. Because of cloudiness, no data are available

along the periphery of the ice sheet below 2000-m ele-

vation, where much of the melting occurred. The avail-

able observations, mostly above 2000 m, show an increase

of surface elevation along the central ridge, especially the

Summit, of Greenland, and a decrease of elevation on the

slope west of the Summit. In contrast, the model shows

a small decrease in ice surface elevation along the cen-

tral ridge of the GrIS, presumably because of an under-

estimated increase of rainfall along the narrow central

ridge by the NCEP–NCAR reanalysis with coarse spa-

tial resolution (2.58). To the east of the Summit and over

the South Dome, the model shows increased ice surface

elevation, which agrees qualitatively with observations.

The comparison of ice surface elevation change empha-

sizes the importance of high-resolution climate forcing,

especially of snowfall, for realistic modeling of the ice

accumulation rate.

3472 J O U R N A L O F C L I M A T E VOLUME 24

The Fig. 3 inset compares the modeled total mass loss of

the GrIS driven by the NCEP–NCAR reanalysis with that

of GRACE. For the period April 2002 to September 2008,

the rate of total ice mass loss agrees well between the model

and observations, both showing about 2147 km3 yr21 over

the 2002–08 period. However, the model shows clearer

and stronger seasonal cycles and interannual changes

compared with those suggested by GRACE. We notice

that an updated ice changing rate, covering April 2002-

November 2009, is about -219 km3 yr-1, with an uncertainty

level of 40 km3 yr-1 (Chen et al. 2011). Compared with this

series provided by the same research group, new method

of leakage correction is applied based on linear projection.

This new rate is closer to the model estimation.

The comparison with satellite observations of the max-

imum SME, ice surface elevation change, and total ice

mass loss of the Greenland Ice Sheet suggest that our ice

model is able to realistically simulate spatial patterns

and trends of maximum SME and of total ice mass loss

over the past two decades at least, for periods when ob-

servations are available. An increase in surface elevation

along the central ridge of Greenland, as suggested by the

GLACE/ICEsat, is not captured by the model possibly

because of the low resolution of the climate input. The

seasonal and interannual variations of the total ice mass

loss also are larger than those from GRACE.

4. Projected changes in Greenland Ice Sheet for thetwenty-first centuries

We use the surface climate conditions provided

by CCSM3 and MIROC3.2, high-resolution version

[Miroc3.2(hires)], respectively, to drive the ice model

and simulate the summer season melt area, ice surface

FIG. 1. (top) Observed and (bottom) simulated maximum melt surface area extent for 1992 and 2002—(a),(b)

adapted from Chapter 6 in ACIA2005 and originally from Konrad Steffen, CIRES/University of Colorado at

Boulder. Melting areas are in red. For (c),(d) the 2000-, 2500-, and 3000-m elevation contours also are shown.

1 JULY 2011 R E N E T A L . 3473

elevations, flow pattern changes, and total mass loss of

the GrIS over the twentieth and twenty-first centuries.

Such an extensive simulation period is necessary be-

cause the high-latitudinal North Atlantic has significant

interdecadal and multidecadal variability (Wallace 2000).

It also allows an evaluation of the changes in the twentieth

century and a comparison of future changes with the re-

cent past. For brevity, we focus only on results from

CCSM3 in our discussion, and show corresponding results

from MIROC3.2(hires) only when there are major dif-

ferences present.

For the twentieth century, we use the twentieth-century

climate in coupled models (20C3M) runs (forced by ob-

served anthropogenic and external climate forcing) of

the CCSM3 and MIROC3.2(hires) to drive the ice model.

For the twenty-first century, we use predicted surface

climatic changes under SRES A1B scenario from these

two CGCMs as inputs to the ice dynamics model.

Figure 4 shows the monthly mean surface temperatures

and precipitation for the period of 1900 to 2100. The an-

nual maximum surface temperature averaged over the

GrIS lies between 270 and 275 K for the period 1990–

2050 (Fig. 4a). The season with this near-freezing-point

annual maximum temperature, referred to as the melting

season, was confined to early June–early August period

for much of the twentieth century until the 1980s. Since

then, the melting season has expanded to the period of

late May–mid-August by year 2000 and will expand to

the period of mid-May–early September by year 2050.

For the period 2050–2100, the areal mean annual max-

imum surface temperature over the GrIS should rise

above 275 K, well above the freezing point. The melting

season also expands rapidly by 2100 to early May–late

September. Figure 4c shows that the annual mean surface

temperature averaged over the GrIS rises by about 6 K

(CCSM3) (or 5 K, MIROC) during the twenty-first cen-

tury. Modeled precipitation shows annual maxima gen-

erally during August–November, fluctuating between July

and December, on decadal to multidecadal scales during

the twentieth century (Fig. 4b). This rainy season is length-

ened to mid-May/April of the following year during the

period 2050–2100 and the annual snow precipitation rate

also increases by up to 27% (Fig. 4d). Different climate

models exhibit a large spread in projecting regional cli-

mate. Other CGCMs in the IPCC AR4 archive were

examined for their projections of temperature and pre-

cipitation under the A1B emissions scenario. CCSM3 and

MIROC3.2(hires) were chosen here as they are repre-

sentative of the intermodel spread.

Because of the strong dependence of ice viscosity on

temperature, it is important to obtain an accurate sim-

ulation of the temperature regime. In Fig. 5, we compare

ice model simulated temperatures with corresponding

FIG. 2. Elevation change rates, averaged between 2002 and 2007.

The color scales are in centimeters per year. (a) For ICES at ob-

served elevation change between 2003 and 2007, the level II

(GLA06XX) data are used. Data are quality controlled by re-

moving pixels with cloud flags . 3 and elevation flags . 32. Those

white spaces are grids lacking valid data.

FIG. 3. Net mass balances of the Greenland ice sheet in the

twentieth and twenty-first centuries. Comparisons are among using

two CGCM provided meteorological conditions: MIROC3.2(hires)

(dot line) and CCSM3 (solid line), NCEP reanalysis provided me-

teorological conditions, and GRACE observations (red dashed line).

The inset is a zoom-in for the past decade. Comparisons are between

model simulation using NCEP reanalysis provided meteorological

conditions (black line) and GRACE measurements (red line). Be-

cause GRACE measurements are only meaningful as relative values

compared with the starting point, we shifted the curve so that the

two curves have the same value at the first measurement time of

GRACE. We notice that an updated ice changing rate, covering April

2002-November 2009, is about -219 km3 yr-1, with an uncertainty level

of 40 km3 yr-1 (red cross; adapted from Chen et al. 2011).

3474 J O U R N A L O F C L I M A T E VOLUME 24

FIG. 4. Area-averaged (a),(c) temperature and (b),(d) precipitation rate over Greenland from the CCSM3 model

simulation. (top) The variations in each month and (bottom) the annual-mean time series of the area-weighted (c)

surface air temperature, and (d) precipitation rate. Thick curves in (c) and (d) are 21-yr low-pass-smoothed repre-

sentations of the corresponding annual series. The two vertical redlines define the period corresponding to the recent

survey, (a),(b) illustrate the course of annual values of month-by-month temperature/precipitation rate averaged

over Greenland, putting the survey period into a long-term perspective. The (c) annual mean temperature increases

by ;48C over the next century while (d) the annual mean precipitation increases by 0.3 mm day21. The CCSM3

model time series in (c),(d) are indicated by red curve, and MIROC model time series are indicated by black curve.

1 JULY 2011 R E N E T A L . 3475

borehole records (Cuffey et al. 1995). As the grid points

of the ice model do not coincide with the borehole loca-

tions, the average value of the four nearest grids, weighted

by the inverse distance from the borehole, is compared

with the actual borehole observations. The initial starting

temperature profile provided by the SICOPOLIS agrees

well with the Greenland Ice Sheet Project 2 (GISP2)

borehole observations for all depths (not shown). In the

upper 1500 m, the signature from the Little Ice Age

(top), the mid-Holocene warmth, and the cold glacial

period (near bottom) are evident in both profiles. Starting

from this initial temperature profile, our model predicts

a future temperature profile at year 2100 shown in Fig. 5.

The shallow warming spike at the top is due to the warming

trend over the twenty-first century. For the bottom half

of the ice column, the differences are generally less than

0.18C. The shallow warming spike at the top is due to the

warming trend over the twenty-first century. The tem-

perature trend in the future 100 years reaches 1500 m,

far deeper than the 35 m allowed by diffusion processes.

Comparing respective contributions from different heat-

ing terms reveals that advection and diffusion terms both

are an order of magnitude smaller than the strain heating

term because of the enhanced surface flow speed. For the

top 100 m, vertical advection contributes significantly,

whereas heating deeper than 100 m is primarily due to

strain heating (;10 K kyr21).

Figure 6 shows the projected maximum SME by both

CGCMs. There are no permanently frozen surfaces south

of 688N (Figs. 6a and 6b). South of 758N, the melting ex-

pands inland and approaches the 2500-m elevation con-

tour, while on the colder northern side it generally reaches

the 2000-m contour. Centered on the intersection of the

748N and 388W, the melt area increases steadily after

2020 and extends to ;1 3 106 km2 by 2100, with the

melting front surpassing the 2600-m elevation contour,

leaving only ;7 3 105 km2 of frozen surface area sur-

rounding the summit. The two CGCMs project a very

similar pattern for increased SME.

Figure 7 shows the projected change in ice surface

elevation from the two CGCMs between 2060 and 2000.

Despite the difference in magnitudes (MIROC3.2 pro-

duces a greater mass loss than CCSM3), both CGCMs

predict strong peripheral mass loss, especially along the

western peripheral area, and along the southwestern

edge following the basal sliding pattern. The central por-

tion of the ice sheet experiences little elevation change. In

some regions, there is an increase in elevation because of

increased wintertime snow precipitation. Snow accumula-

tion is highest in the southeast. This region maintains its ice

elevation primarily due to increased winter precipitation

that offsets the increased ice flow and summertime melt-

ing. However, the net ice elevation change in this region

could vary strongly on annual and decadal time scales due

to changes of precipitation (Krabill et al. 2000). The ice

elevation over the summit is highly stable under the future

atmospheric conditions simulated by the MIROC3.2(hires)

and the CCSM3.

Figure 8 shows modeled surface velocity fields for

year 2000 and also the changes between 2060 and 2000.

Within each ice divide (hereafter we follow the con-

vention of Zwally and Giovinetto 2001), the flow speed

increases from the central ridge toward the grounding

line. For the northeastern Greenland ice stream (region

II of Zwally and Giovinetto 2001) and the Jacobshavn

Isbræ in central-western Greenland (the narrow conver-

gent region along the 688N parallel in region V of Zwally

and Giovinetto 2001), our modeled surface velocity in year

2000 is close to the European Remote Sensing-1 (ERS-1)

satellite-observed large flow features (Fahnestock et al.

1993). The concentrated ice flow of Jacobshavn Isbræ

mainly is from the ice dynamics arising from bed geometry

and ice thickness profile. The formation of the northeast

Greenland ice stream primarily is due to bedrock geomor-

phology and ice geometry and, to a lesser degree, geo-

thermal heat flux from the bottom.

Over most of the peripheral area, the surface ice flow

change is an order of magnitude greater than explain-

able from local elevation changes. The large change in

ice flow is due to elevated temperature that reduces ice

FIG. 5. Comparison of measured (dashed line) and modeled

(solid lines) temperature within the ice sheet, as function of depth

below surface (the thickness of the ice sheet is about 3044 m). The

differences deeper than 2000 m are minimal. There are 12 monthly

output profiles for year 2100. The spread (seasonality) is limited to

the upper 10 m (indistinguishable at this vertical scale of display).

The temperature trend in the future 100-yr period is apparent down

to 1500 m, far deeper than diffusion processes can reach. The narrow

warming spike at the top is due to warming of the twenty-first

century.

3476 J O U R N A L O F C L I M A T E VOLUME 24

viscosity and causes nonlocal flow pattern changes. The

ice thickness shrinks most for ridges in the peripheral

areas because the downstream mass deficit enhances ice

flow divergence. For some peripheral areas, strong sur-

face melting (land based) and calving (extending to

open waters) causes up to a 1 m yr21 elevation decrease

despite weaker ice flow divergence in the southwest

corner of Greenland (Fig. 7).

To quantitatively compare ice flow changes between

years 2000 and 2060, we plotted the u component

FIG. 6. Projected maximum melt surface area extent by 2060—adapted from (a) CCSM3 and (b) MIROC. Melting

areas are in red. The 2000-, 2500-, and 3000-m elevation contours also are shown for location reference.

FIG. 7. Surface elevation changes between 2000 and 2060 for (a) CCSM3 and (b) MIROC(hires). The color scales are

in meters.

1 JULY 2011 R E N E T A L . 3477

velocity for grid points above 1500-m elevation for these

two years (Fig. 8b). The majority of the flow samples are

located in quadrants I and III, suggesting no direction

change in ice flow over much of Greenland. The distri-

bution of these samples is along a line with slope 1.09,

indicating that the flow magnitudes increase on average

by 10% over the next 50 years. More than fifty grid points

(;0.4% relative to total grids) are located in quadrants II

and IV, suggesting changes in flow direction between

2000 and 2060. Region by region analysis indicate that,

by the year 2060, the largest changes in the flow fields are

over the northeast (ice divide II) and the southern tip. All

ice discharge streams become more concentrated. For ice

divide II, the modeled surface velocity at year 2000 re-

produces all primary features of the observed surface

velocity (Joughin et al. 2001). Examination of the ice

surface flow field of year 2060 reveals that, for most of

the inland area, the surface flow speed is generally less

than 200 m yr21. However, for drainage divide II, max-

imum speeds of ;600 m yr21 occur near the grounding

lines. A cautionary note is that the ice-flow velocity in the

narrow, fast-moving outlets cannot be compared with our

model results here because our model spatial resolution is

too coarse to resolve the stress discontinuity.

Figure 3 shows the modeled total ice volume change

forced by surface climate conditions provided by both

CGCMs for the twentieth and twenty-first centuries.

The total ice volume obtained from using NCEP–NCAR

reanalyses provided atmospheric parameters and GRACE

observations, respectively, also is plotted as references for

assessing the realism of the changes in total ice volume

as determined by the CGCMs. The absolute values are

somewhat arbitrary and only the rates of ice volume

change are comparable to the observation and that ob-

tained from NCEP–NCAR reanalysis. Both CGCMs

underestimate the rate of the total ice volume loss com-

pared to those suggested by GRACE and NCEP–NCAR

reanalysis for the period of 2002–08 and 1970–2008, re-

spectively. The projected rates of total ice mass loss also

are different between the two CGCMs for the period of

2010–65 with CCSM3 showing no net ice mass loss until

2050. The MIROC3.2(hires) shows a net mass loss rate

of ;50 km3 of ice per year for the period of 2000–50 and

reaches ;220 km3 of ice per year after 2050. The zero

or slow rate of total ice mass loss during the first half of

the twenty-first century is due mainly to increased pre-

cipitation, primarily in the interior of the Greenland,

which compensates for the ice mass loss due to increased

FIG. 8. (a) The model-simulated surface velocity field (year 2000), and (b) a scatterplot of the u component of velocity, year 2000

(horizontal axis) vs year 2060 (vertical axis).

3478 J O U R N A L O F C L I M A T E VOLUME 24

melting in the periphery of the ice sheet. Because the ice

mass change at this stage is dominated by changes in sur-

face climate conditions, the large discrepancy in the total

ice mass loss between the two CGCMs is due to differ-

ences in projected climate change, especially change in

precipitation, over Greenland. However, after year 2065,

both CGCMs project similar rates of rapid ice mass loss

because ice flow divergence (enhance by basal sliding and

upper surface warming) dominates ice mass loss by the

late twenty-first century. Projected surface climate dif-

ferences from the two CGCMs have a secondary impact

on total Greenland ice mass loss.

We further compare total ice volume changes under

three different basal conditions (figure not shown): no-

slip, the Weertman-type sliding (Weertman 1957, 1983),

and granular-type basal sliding using atmospheric pa-

rameters projected by CCSM3. The Weertman type of

sliding refers to pressure melt at the bottom, for example,

the huge overlying weight caused pressure melt at the

bottom, whereas the granular-type basal sliding refers to

the mechanism as described in MacAyeal (1992). Gran-

ular material will be produced by the meltwater erosion

on bedrock. The saturated granular material usually is

unstably poised on slopes and causing extra basal move-

ment. The effects of basal sliding are small before 2030.

Then, as temperatures continue to rise, the basal sliding

mechanism becomes significant, especially beneath the

southern tip and the northeast ice stream, and signifies

a faster mass shed. The differences between the two basal

sliding schemes are insignificant prior to 2060. Afterward,

the granular basal sliding scheme signifies a far more ef-

ficient mechanism for mass shed. Switching between the

three constitutive laws (Glen’s, Goldsby and Kohlstedt’s,

and Durham’s flow laws) does not change this conclu-

sion. Using the output of the MIROC3.2(hires) as cli-

mate forcing gives qualitatively similar results.

It is important to note that as it is a coupled system,

the effects of basal sliding do not abruptly ‘‘kick in’’ at

a certain time (e.g., at the year 2030). Basal sliding is but

one link of a positive feedback chain. Basal sliding is

present throughout the simulation and helps warm the ice

from inside. Also, it is related to the surface meltwater

being channelled into the granular layer (especially in the

marginal areas), because granular viscosity is liquid-water-

content sensitive (Eq. (3) in Appendix). The total mass

balance is a bulk metric. Here just describe the ‘general’

behavior of the total mass change curve (that after 2030

becomes more noticeably different from that without

consideration of basal sliding).

For comparison, we also computed the ice mass loss by

the end-of-twenty-first-century carbon emissions for two

other emissions scenarios A2 (high) and B1 (low), in ad-

dition to the A1B (moderate) scenario. Carbon emissions

for these three scenarios range from 5 gigatons of carbon

(GtC) yr21 for B1 up to 29 GtC yr21 for A2, with cor-

responding atmospheric CO2 concentrations lie between

;500 to ;900 ppmv. The mass loss appears to scale with

the atmospheric CO2 concentration, such that the curve

obtained under the A2 scenario shows faster melting

than under A1B. Conversely, B1 is a slower melt version

than found here. The patterns of geographical change

are relatively consistent across all emission scenarios.

For the connected ice regime, no stress discontinuities

exist in the ice divides over the entire twenty-first cen-

tury. Consequently, our simulations show a gradual loss

of ice mass in the entire twenty-first century. Our result

cannot be used to suggest that the response of the GrIS

to climate warming must be gradual in reality.

5. Conclusions

In this study, we investigated the melting of the

Greenland ice sheet (GrIS) during the twentieth and

twenty-first centuries and the underlying mechanisms,

using a new ice dynamics model, SEGMENT-Ice,

forced by monthly atmospheric conditions provided by

high-resolution climate models. This new ice model is

based on the full Navier–Stokes equations that account

for nonlocal dynamic balance, and its influence on ice

flow and also includes a granular sliding layer between

the bottom ice layer and the lithosphere layer to pro-

vides a mechanism for large scale surges in a warmer

future climate. The monthly climate forcing for this ice

sheet model allows an investigation of detailed features

such as seasonal melt area extent over Greenland. The

model driven by climate conditions from the NCEP–

NCAR reanalysis also reproduced reasonably well the

annual maximum SME and total ice mass lost rate

when compared with those observed by the SSM/I and

GRACE.

Simulations of this ice dynamic model are forced by the

outputs of the NCAR CCSM3 and MIROC3.2(hires) for

the twentieth century ‘‘anthropogenic-external forcing’’

simulations and the twenty-first century simulations un-

der the IPCC moderate emission scenario SRES A1B.

The 200-yr simulations allow us to assess impact of

anthropogenic-induced warming on mass loss of the

GrIS, despite strong decadal and multidecadal natural

climate variability. The results suggest that before year

2060 the total mass loss of the GrIS should be relatively

slow (;50 km3 yr21) and changes of the net balance

between the increases of summer surface melting and that

of winter precipitation dominate such an ice mass loss.

After 2060, the total ice mass loss accelerates rapidly to

;220 km3 yr21. The accelerated ice flow and granular

basal sliding, due to subsurface positive feedback between

1 JULY 2011 R E N E T A L . 3479

the strain heating and increase of ice flow, becomes

dominant and changes in surface climate conditions

become less influential. These results highlight the im-

portance of greenhouse gases emissions and temperature

increases in the models during the first half of the twenty-

first century.

The model results indicate that changes in ice velocity

can be forced by changes in subglacial mechanics as well

as upper-boundary thermal regime changes, and geometric

transitions are governed by changes in flux divergence as

well as surface mass balance. This conclusion is espe-

cially relevant for a future warming climate.

Calculation of trends is vital in determining whether

the observed net mass loss trends continue beyond the

survey period. Despite the high climate variability of the

high-latitude North Atlantic region, the surveyed melt-

ing is attributed primarily to climate warming. Both

accumulation and melt rates increase and counteract

each other for net mass balance, with an overall negative

mass balance. By 2100, the perennial frozen surface area

decreases by up to 60%, indicative of a serious expan-

sion of the ablation zone. Ice flow speeds are sensitive to

warming. With enhanced surface flow, strain heating

increases dramatically and propagates warming effects

much deeper than achievable by diffusion alone. Our

results show the importance of basal sliding, especially

involving granular material, which has been a previously

neglected mechanism for fast glacier acceleration and

accelerated mass loss. The fact that two independent

CGCMs give such similar results adds confidence to our

conclusions for longer time scales (.50 years).

Acknowledgments. This work is supported by the

Gary Comer Science Foundation, the Jackson School of

Geosciences, the University of Texas at Austin, and the

NASA OVWST subcontract from JPL. We thank Pro-

fessors R. Alley for providing the GISP2 borehole data,

R. Greve for offering the SICOPOLIS model code, and

Van der Veen for providing the force balance model code.

The first author also thanks Dr. Jezek for his insightful

comments on the possible importance of the advection and

inertial terms for the ice flow model. Molly McAllister and

David Korn from the National Snow and Ice Data Center

(NSIDC) helped with the 5-km DEM and ice thickness

data. We acknowledge the international modelling groups

for providing their data for analysis, the Program for Cli-

mate Model Diagnosis and Intercomparison (PCMDI)

for collecting and archiving the model data. Transient

climate simulations under SRES A1B were obtained from

the PCMDI Coupled Model Intercomparison Project

(CMIP). These simulations were run as part of a coordi-

nated series of simulations by the modelling centres for

the IPCC Fourth Assessment Report.

APPENDIX

Description of the Ice Sheet Model

This section includes a derivation of the 3D granular

rheology law in the context of lithostatic and resistive

decomposition, consistent choices for the ice constitutive

law and Weertman basal sliding scheme, and the unique

treatments of surface melting rate and runoff.

We propose a new ice dynamics model, SEGMENT-

Ice, based on the incompressible Navier–Stokes formu-

lation. In standard notations, the mass conservation

equation is

$ �V 5 0 (A1)

and the momentum conservation equation is

r

�›V

›t1 $ � (V 3 V)

�5 $ � s 1 F, (A2)

where r is the density, V is the velocity vector, s is the

internal stress tensor, and F is the body force (e.g.,

gravity rg). Instead of using the standard decomposition

of the full stress tensor s into static and dynamic stress

parts, we decompose it into lithostatic (L) and resistive

(R) parts (Van der Veen 1999; Van der Veen and

Whillans 1989): sij

5 Rij

1 dijL, where Rij denotes the

components of the resistive tensor, and d is the Kro-

necker operator. This continuum-mechanical formula-

tion is improved further by including acceleration and

advection terms for ice motion (Ren et al. 2008).

As a non-Newtonian fluid, polycrystalline ice has

a shear-thinning rheology in which the strain-rate is

proportional to the applied deviatoric stress raised to an

exponent (Glen 1955). This proportionality is tempera-

ture dependent (Goldsby and Kohlstedt 2001; Paterson

1994) and follows the parameterization in Hooke (1981).

For the Greenland ice domain, this parameterization gives

a viscosity range of 4 3 1014–1.1 3 1015 Pa s. From several

possibilities (Goldsby and Kohlstedt 2001), we choose

Glen’s constitutive relationship because it has proven to

be acceptably accurate for studying the large-scale flow

characteristics of real glaciers (Van de Veen 1999) and

therefore should provide good estimates of total mass

loss and overall changes in the surface elevations.

The movement of glacial ice is achieved by a combina-

tion of plastic flow, sliding, and the deformation of un-

derlying basal sediments. Pressure-melted water plays

an important role in each of these processes. Weertman

(1957, 1983) showed how the rate of ice sliding at the local

pressure melting temperature (PMP) depends on scales

of roughness elements on the glacier bed. However, the

3480 J O U R N A L O F C L I M A T E VOLUME 24

original form of Weertman’s law does not fit into the

framework of field dimension sliding (Hooke and Iverson

1985), nor does it treat the frictional stresses exerted by

entrained sediment particles, which have been identified

as important contributors to the overall shear stress at the

bed (MacAyeal 1992; Hooke and Iverson 1985). The

liquid-like layer separating the ice from the bedrock exists

even for glaciers far below the bulk PMP at their beds

(Gilpin 1979). This concept has been adopted by mod-

ellers and has been observed in the field (Shreve 1984;

Hallet 1996). The ‘‘grade-glacier’’ theory (Alley et al.

2003) generalizes silt production and transportation as an

integrated component of the ice erosion on glacier bed. It

shows that climate fluctuations, by modifying ice surface

slope, can affect sediment transport and erosion patterns.

This theory directly motivated the present research be-

cause the established warming climate may flatten the

marginal area of the fast glaciers surrounding the Green-

land ice sheet and therefore encourage the deposition of

granular sediments.

A Weertman-type sliding law, with overburden pres-

sure corrected for the subglacial water buoyancy, appears

well-suited for describing large-scale flow features (see the

review in Bindschadler 1983). This makes it appealing to

be used together with Glen’s law. We follow the treatment

of basal sliding coefficient Cb in the SICOPOLIS. The

crevasses and moulin distribution (Zwally et al. 2002) may

signify an important mechanism for surface meltwater

drainage. Owing to a lack of survey data and large un-

certainties in their distribution characteristics, it is diffi-

cult to directly parameterize their effects on basal sliding.

Therefore, we follow an empirical approach, which uses

a surface meltwater coefficient, g, usually between 0 to

6 yr m21, to enhance Cb, using the linear multiplier (1 1

gm), with m being melt rate. The very existence of cre-

vasses is a strong indication of uneven basal erosion, which

produces granular material. When Weertman sliding is

activated, we separate a granular layer from the bottom

bedrock. Unlike ice, the viscosity of granular material

depends also on the isotropic stress. For this granular

sublayer, a newly proposed rheology (Jop et al. 2006) is

applied, namely,

n 5

�m0 1

m1 2 m0

I0/I 1 1

�S��«:e�� , (A3)

where n is viscosity, S 5 [Rkk 2 rg(h 2 z)]/3 is the

spherical part of the stress tensor s, m0, and m1 are the

limiting values for the friction coefficient m, and m1 and

m0 are liquid water content sensitive. Here, j«:ej is the

effective strain rate and j«:ej 5 [0:5(«:ij � «:ij)]0:5, I0 is

a constant depending on the local slope of the footing

bed as well as the material properties, and I is inertial

number defined as I 5 j«:ej d/(S/rs)0:5, where d is particle

diameter and rs is the particle density. The granular

layer thickness, basal material density, and the effective

particle size are determined optimally using the datum

period. If the retrieved thickness is less than 5 cm, the

granular layer is nominal and is not activated. Applying

the constitutive relationship reduces the unknowns in

Eq. (A2) to the three velocity components (u, y, and w).

Based on conservation of mass, momentum and energy,

originally nonglaciated grids can be glaciated and vice

versa.

We use the following thermal equation (Greve 2005):

rc

�›T

›t1 (V � $)T

�5 kDT 1

2

ns2

eff, (A4)

where c is heat capacity [(J kg21) K21], T is temperature

(K), k is thermal conductivity [W K21) m21], and seff is

effective stress (Pa). The last term is ‘‘strain heating’’ or

the converting of work done by gravity into heat used to

heat the sliding material or cause phase change.

The dynamic [Eq. (A2)] and thermodynamic [Eq. (A4)]

equations are coupled. The upper-boundary condition for

Eq. (A2) is that of free stress. The zero-velocity gradient is

applied as a lateral boundary condition. The boundary

conditions for Eq. (A4) are a surface temperature at top of

each grid [Tjz5zt

5 Ts(x, y)] and a geothermal flux to the

base of the lithosphere layer [k(›T/›z)jz5zb

5 G0, here

G0 is geothermal heat flux (W m22)].

The phase change of surface ice is simulated using an

energy balance–based melt model (Ren et al. 2007). It

takes the surface net radiation and the current state of

the surface layer as input. The model then estimates the

latent and sensible heat fluxes and budgets the mass

within each time step. The ground heat flux is used as an

upper-boundary heating/cooling to diagnose the ice tem-

perature. We integrate a prognostic equation that includes

full-3D heat advection, internal friction, and heat diffusion

to estimate the temperature profile within the ice regime.

A semi-implicit temperature solver automatically adjusts

iteration time steps within a ‘‘big’’ time step of 24 h. The

thinner the layer depth is, the more time consuming is the

iteration process. To lessen the computation load, regions

with total ice thickness less than 50 m are treated here as

a bulk layer for temperature prediction.

For the net mass balance of the ice sheet, arguably the

most important quantity is the runoff. We assume a total

withholding of the mass for snow falling on the dry snow

zone and percolation zone (Benson 1962). Melting water

from the ablation zone is assumed to be lost in a manner

analogous to water drainage from a porous soil layer. The

analogy is between firm and sandy soil. This also applies to

other cases involve water redistribution among grids (e.g.,

1 JULY 2011 R E N E T A L . 3481

ponding water and mixed form of precipitation). We use

a carefully edited digital mask (referenced to the zones

division in Benson 1962) to investigate the refreezing of

meltwater and hence to gain improved estimation of the

net runoff. Because the form of precipitation under a

warming climate may not strictly follow this mask, we

assign higher weighting to the surface temperature to

determine the precipitation forms. For possible rainfall in

the ablation zone, an important mixing process is included

[viz., the Qm term in Eq. (1) of Ren et al. (2007)], be-

cause heat transferred to snow by rain during cooling to

08C is significant (Peng et al. 2002). The GRACE mea-

surements indicate that post glacial rebound (PGR) is

not a significant issue within the GrIS range (Fig. 2 in

Chen et al. 2006).

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